348
A. Gerocs et al.
Fig. 5 Campbell diagram
the difference between the experimental and computed results does not exceed 6%.
This confirms that the 3D model, the assumed material properties and the boundary
conditions were correct set, as the simulation results are validated by comparing
them with the experimental data.
The differences between the eigenfrequencies obtained by experimentation
and FEA may be generated by some differences between the material properties, primarily mass density, Poison’s ratio and elastic modulus, ahead with mass
differences caused by the geometrical irregularities of the real housing.
Finally, the Campbell diagram was employed for localizing and mapping the
resonant frequencies of the housing. Being a mathematically constructed graph, the
Campbell diagram is an important tool in assessing the dynamic behavior of rotating
machines. It plots frequency versus rotational speed and is used to check coincidence
of natural frequencies with vibration sources. Thus, critical speed may be identified
if the natural frequency line intersects the exciting frequency (in case of gear systems
the teeth engagement frequency) line. If there are intersections of these lines in the
Campbell diagram, they lead to resonance, a phenomenon that must be avoided.
Figure 5 presents the Campbell diagram for the investigated housing. With horizontal lines are plotted the first six natural frequencies (f o1 , f o2 , …, f o6 ), while the
inclined lines show the variation of the first three harmonics of the teeth engagement
frequencies (f z1 , f z2 and f z3 ) depending on the gearbox driving speed.
As it can be observed, in the operation speed range of the gearbox (n 1 = 1000 −
1500 rpm—see Table 1), which is delimited in the diagram by a rectangle drawn with
dashed black lines, some converging points marked with red color triangles appear
at the intersections between the natural frequency lines and the excitation frequency
lines. There were identified five critical speeds.
Commonly, not all diagnosed critical speeds are equally alarming. A reason for
this is the fact that probably some natural frequencies of the higher modes do not
occur as compelling vibrational peaks in the system. Furthermore, the situation may
arise, when more critical speeds are detected in the Campbell diagram, but they don’t
A. Gerocs et al.
Fig. 5 Campbell diagram
the difference between the experimental and computed results does not exceed 6%.
This confirms that the 3D model, the assumed material properties and the boundary
conditions were correct set, as the simulation results are validated by comparing
them with the experimental data.
The differences between the eigenfrequencies obtained by experimentation
and FEA may be generated by some differences between the material properties, primarily mass density, Poison’s ratio and elastic modulus, ahead with mass
differences caused by the geometrical irregularities of the real housing.
Finally, the Campbell diagram was employed for localizing and mapping the
resonant frequencies of the housing. Being a mathematically constructed graph, the
Campbell diagram is an important tool in assessing the dynamic behavior of rotating
machines. It plots frequency versus rotational speed and is used to check coincidence
of natural frequencies with vibration sources. Thus, critical speed may be identified
if the natural frequency line intersects the exciting frequency (in case of gear systems
the teeth engagement frequency) line. If there are intersections of these lines in the
Campbell diagram, they lead to resonance, a phenomenon that must be avoided.
Figure 5 presents the Campbell diagram for the investigated housing. With horizontal lines are plotted the first six natural frequencies (f o1 , f o2 , …, f o6 ), while the
inclined lines show the variation of the first three harmonics of the teeth engagement
frequencies (f z1 , f z2 and f z3 ) depending on the gearbox driving speed.
As it can be observed, in the operation speed range of the gearbox (n 1 = 1000 −
1500 rpm—see Table 1), which is delimited in the diagram by a rectangle drawn with
dashed black lines, some converging points marked with red color triangles appear
at the intersections between the natural frequency lines and the excitation frequency
lines. There were identified five critical speeds.
Commonly, not all diagnosed critical speeds are equally alarming. A reason for
this is the fact that probably some natural frequencies of the higher modes do not
occur as compelling vibrational peaks in the system. Furthermore, the situation may
arise, when more critical speeds are detected in the Campbell diagram, but they don’t